This paper investigates the controllability relationship between node and edge dynamics in undirected signed graphs of multi-agent systems. First, dynamic models for nodes and edges are constructed using a social network case study. Next, the concept of bidirectional edge mapping is introduced, and an associated matrix is established to analyze the relationship between the node and edge Laplacian matrices. Additionally, criteria for determining the controllability relationship between node and edge dynamics are presented for three cases, based on the numerical relationship between the number of nodes n and edges m (i.e., $$n>m$$ , $$n=m$$ , and $$n